The companies disclosed Monday that Pfizer in January made a cash-and-stock offer of £46.61 ($78.45) a share to acquire AstraZeneca, which rejected the bid. Pfizer renewed contact over the weekend without making a new bid.

A Pfizer-AstraZeneca acquisition would be the biggest “inversion deal”—in which a U.S. company buys a smaller player in a more-favorable tax jurisdiction and reincorporates there—yet transacted. Previous examples, all to reincorporate in Ireland, include Actavis’s $5 billion takeover of Warner Chilcott and Perrigo’s $8.6 billion takeover of Elan.

Marc Booty, head of health care at Pictet Asset Management, said he thinks U.S. political risk is high. Signing of any deal would be followed by months of likely uncertainty during which the U.S. might change its rules on inversion deals, he said.

“My question is, if I’m a long-term investor, do I want that deal happening?” Mr. Booty said. “How sustainable is it to take tax out of the U.S. system and then still expect the U.S. to pay out 19% of its [gross domestic product] on health care?”

Dan Mahony, a health-care fund manager at Polar Capital, said he also sees political risk as a factor and thinks a Pfizer-AstraZeneca deal could be a catalyst for changes to the U.S. tax system.

Mr. Mahony said he thinks a bid of £50 to £55 a share would be high enough to interest most AstraZeneca shareholders, given expected falls in AstraZeneca’s sales in coming years from drugs losing patent protection. It also would price in reasonable assumptions for AstraZeneca’s drug-development pipeline, he said.

“This stock was about £30 this time last year and it’s not as if Astra’s problems have evaporated—you still have this big, looming patent cliff for both Nexium and Crestor,” Mr. Mahony said.

If Pfizer does renew its bid interest, one AstraZeneca defense strategy could be to seek an alternative takeover partner.

Much of AstraZeneca’s attraction for a would-be bidder lies in its broad pipeline of cancer drugs in development. Pfizer isn’t in the top five drug companies in cancer treatments by market share, lying behind market leader Roche Holding as well as Novartis, AstraZeneca, Eli Lilly, Johnson & Johnson and Bristol-Myers Squibb, despite blockbuster sales expectations for a breast-cancer treatment it is developing called palbociclib.

U.S. companies such as Amgen or Abbvie might like to bolster their “immuno-oncology” portfolios through a tie-up with AstraZeneca, Citigroup analyst Andrew Baum said. Novartis, which last week announced a $14.5 billion acquisition of GlaxoSmithKline’s cancer-drug portfolio, might be in a similar position.

Still, health-care investors and analysts are struggling to name a clear “white knight” candidate.

“Pfizer has a very strong track record of taking out costs in the deals that it’s done,” Mr. Booty said. “So if they don’t feel that the deal stacks up purely on the synergies and keeping its U.K. tax code, then I don’t see anyone else doing it better.”